Question

Evaluate: `int x/(x^2 + 1)"d"x`

Options

• 2log(x² + 1) + c

• `1/2`log(x² + 1) + c

• `"e"^(x^2 + 1) + "c"`

• `logx + x^2/2 + "c"`

Answer 1

`bb(1/2log(x^2 + 1) + c)`

Explanation:

`int x/(x^2 + 1)"d"x`

= `1/2 int "dt"/"t"`

= `1/2 log "t" + "C"`

= `1/2 log (x^2 + 1) + "C"`

Put x² + 1 = t

2x dx = dt

x dx = `"dt"/2`  ...(i)